Pith Number

pith:3HL2UPNP

pith:2011:3HL2UPNPUV5LAQGIBRAYX2KFZP

not attested not anchored not stored refs pending

A T(1) theorem on product spaces

Paco Villarroya, Sandra Pott

arxiv:1105.2516 v6 · 2011-05-12 · math.CA

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{3HL2UPNPUV5LAQGIBRAYX2KFZP}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:32:28.748702Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

d9d7aa3dafa57ab040c80c418be945cbd32d83e339037508764c5886aa269a54

Aliases

arxiv: 1105.2516 · arxiv_version: 1105.2516v6 · doi: 10.48550/arxiv.1105.2516 · pith_short_12: 3HL2UPNPUV5L · pith_short_16: 3HL2UPNPUV5LAQGI · pith_short_8: 3HL2UPNP

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/3HL2UPNPUV5LAQGIBRAYX2KFZP \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: d9d7aa3dafa57ab040c80c418be945cbd32d83e339037508764c5886aa269a54

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "6ab7650d279a5800ee5f48c6768a23509a6afb6117aff4c1793c9bb8c153c1e1",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CA",
    "submitted_at": "2011-05-12T16:02:20Z",
    "title_canon_sha256": "8fa699fe90797c244fdeecc69b21c150a5743c06a555763b07eb6e8f0f257187"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1105.2516",
    "kind": "arxiv",
    "version": 6
  }
}